Ordinary elliptic curves of high rank over ${\bar{F}}_p(x)$ with constant j-invariant II

Claus Diem, Jasper Scholten

We show that for all odd primes $p$, there exist ordinary elliptic curves over ${\bar{\mathbb{F}}}_p(x)$ with arbitrarily high rank and constant $j$-invariant. This shows in particul…